I don't think this problem is related to the game. I'm using a PS3 controller and i run out of batteries often. I don't need to relog to reconnect my controller and I'm playing in fullscreen too. I think it's related to the drivers you are using.

Try using third party drivers instead of Microsoft's, if they actually exists for the Xbox controller.
I know that if i use the Xbox 360 emulator option in MotionInJoy for my controller, i get the problem you're talking about.

I tried googling to find some drivers but I was not so lucky. Maybe someone will post that uses 3rd party drivers for the controller.